Which function represents a reflection of f(x) = 5(0.8)^x across the x-axis?
g(x) = 5(0.8)^–x
g(x) = –5(0.8)^x
g(x) = (0.8)^x
g(x) = 5(–0.8)^x

The distance between charges of +2.35 and −1.96,  should be approximately 1.566 picometers (pm).

Coulomb's law states that the force (F) between two point charges is given by:

F =[tex]\dfrac{(k \times q1 \times q2)}{r^2}[/tex]

Where:

The electrostatic force between the charges is F

k is Coulomb's constant, approximately equal to 8.99 × 10^9 N m²/C².

The magnitudes of the two charges are [tex]q_1[/tex] and [tex]q_2[/tex].

The distance between the charges is r.

Given that the charges are +2.35 and −1.96, we'll call the distance between them x (in pm). Similarly, for charges +4.06 and −2.11, the distance is given as 2.26 pm.

Setting up the equation:

For the first pair of charges (q1 = +2.35 C and q2 = −1.96 C):

F1 =[tex]\dfrac{(k \times |2.35 \times (-1.96)|)}{x^2}[/tex]

For the second pair of charges (q1 = +4.06 C and q2 = −2.11 C):

F2 =[tex]\dfrac{(k \times |4.06 \times (-2.11)|)}{(2.26)^2}[/tex]

Since the forces are said to be equal, we have:

F1 = F2

The solution of the expression for x is given by:

[tex]\dfrac{(k \times |2.35 \times (-1.96)|}{x^2}[/tex] =[tex]\dfrac{(k \times |4.06 \times (-2.11)|)}{(2.26)^2}[/tex]

|[tex]\dfrac{(2.35 \times (-1.96)}{x^2}[/tex]| =[tex]\dfrac{|4.06 \times (-2.11)|}{ (2.26)^2}[/tex]

[tex]{(2.35 \times 1.96)} {x^2}[/tex] = [tex]\dfrac{(4.06 \times 2.11)} { (2.26)^2}[/tex]

[tex]x^2[/tex] =[tex]\dfrac{(2.35 \times 1.96 \times (2.26)^2} {(4.06 \times 2.11)}[/tex]

[tex]x^2[/tex] = 2.450206485

x ≈ [tex]\sqrt{2.450206485[/tex]

x ≈ 1.566 pm

Therefore, the distance between charges of +2.35 and −1.96,  should be approximately 1.566 picometers (pm).

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To find the distance between charges of +2.35 and -1.96 for the attractive force to be the same, use Coulomb's Law to calculate the force between charges of +4.06 and -2.11 separated by a distance of 2.26 pm. Then solve for the distance using the same formula and the calculated force value.

To find the distance between charges of +2.35 and -1.96 for the attractive force to be the same as between charges of +4.06 and -2.11, we can use Coulomb's Law. The formula for calculating the force between two charges is F = k * (|q1 * q2| / (d^2)) where k is the proportionality constant and d is the distance between the charges.

First, we calculate the force between charges of +4.06 and -2.11. Let q1 = +4.06, q2 = -2.11, and d = 2.26 pm. Plugging these values into the formula, we get:

F = (1/47e) * (|4.06 * -2.11| / (2.26^2))

Next, we can find the distance between charges of +2.35 and -1.96 such that the attractive force is the same. Let q1 = +2.35, q2 = -1.96, and F = the value we calculated earlier. Rearranging the formula to solve for d, we get:

d = sqrt((|q1 * q2| / (F * k)))

In a 30-60-90 triangle, the side opposite the 30-degree angle (s) has a length of "s," and the hypotenuse has a length of "2s."

The side opposite the 60-degree angle is "s√3."

We have,

In a 30-60-90 triangle, the sides are in a specific ratio:

x, x√3, and 2x,

where x is the length of the shortest side (opposite the 30-degree angle).

Step 1:

Identify the shortest side (opposite the 30-degree angle).

Let's assume the length of the shortest side (opposite the 30-degree angle) is "s."

Step 2:

Find the other side lengths.

The side opposite the 60-degree angle is s√3.

The hypotenuse is twice the length of the shortest side, so it is 2s.

Thus,

In a 30-60-90 triangle, the side opposite the 30-degree angle (s) has a length of "s," and the hypotenuse has a length of "2s."

The side opposite the 60-degree angle is "s√3."

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Answer:

I think its 30 as well

Step-by-step explanation:

To subtract the fractions 7 8/9 and 5 3/5, first convert them into improper fractions. Then, adjust them to the common denominator (45 in this case) and subtract to get the answer of 2 13/45.

To begin, we need to convert these mixed fractions (7 8/9 and 5 3/5) into improper fractions. 7 8/9 equals 71/9 (since 7*9 + 8 = 71) and 5 3/5 equals 28/5 (since 5*5 + 3 = 28). Now, we can subtract these fractions by finding a common denominator or a number that 9 and 5 mutually divide into. This number is 45. Therefore, we adjust these fractions to have the denominator of 45, getting 355/45 and 252/45. The subtraction of these adjusted fractions equals 103/45. That can be simplified into 2 13/45.

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Answer:

The answer is actually 5.17 centimeters

Step-by-step explanation:

The question is asking you to calculate the minimum thickness so you have to find the lowest bounds.

The covers are 0.9 mm to 1 d.p so the minimum thickness is 0.85 because that is the lowest bound.

The pages are 0.13 mm to 2 d.p so the minimum thickness is 0.125 as that is the lowest bound.

0.85  x 2 = 1.7 and 0.125 x 400 = 50

50 + 1.7 = 51.7 which is the minimum length.

Final answer:

The minimum thickness of a book with 400 pages, each 0.13mm thick, and two covers, each 0.9mm thick, is calculated to be 53.8mm.

Explanation:

The minimum thickness of a book can be calculated by summing the thickness of the covers and all the pages. We are given that each cover is 0.9mm thick and each page is 0.13mm thick. To find the minimum thickness of the book, we multiply the thickness of each page by the total number of pages and then add the thicknesses of the front and back covers.

To calculate:

Thickness of all pages: 400 pages × 0.13 mm/page = 52 mm

Thickness of both covers: 2 covers × 0.9 mm/cover = 1.8 mm

Total minimum thickness: 52 mm + 1.8 mm = 53.8 mm

The minimum thickness of the book is therefore 53.8 mm.

Answer:

x = -3.75 or 4

Step-by-step explanation:

Multiply by 4x and solve the resulting quadratic in any of the usual ways.

... 4x² = 60 +x

... 4x² -x -60 = 0 . . . . . . . . . . . subtract 60+x

... (x -4)(4x +15) = 0  . . . . . . . . .factor the equation

... x = 4 . . . or . . . -15/4 . . . . . . the values that make the factors zero

_____

Comment on the graph

It is convenient to use a graphing calculator to find the zeros of a function, so it works well to rewrite the equation to be something that is equal to zero. Here, we've subtracted the right side, so we have ...

... f(x) = x - (15/x +1/4) = 0

Yes,[tex]\(30 \times 10^3\)[/tex] is equal to 30,000.

When we have a number written in scientific notation, such as [tex]\(10^3\),[/tex] it means we are multiplying the base (which is 10 in this case) by itself a certain number of times, indicated by the exponent (which is 3 in this case).

So, [tex]\(10^3\)[/tex] means [tex]\(10 \times 10 \times 10\)[/tex], which equals 1,000.

Therefore, when we multiply 30 by [tex]\(10^3\)[/tex], it's equivalent to multiplying 30 by 1,000, which results in 30,000.

30240 are 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times

A number system is defined as a system of writing to express numbers.

By means of Permutation we solve this

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged.

The formula for permutation is [tex]^{n}P_{r} =\frac{n!}{(n-r)!}[/tex]

n is total number of objects

r is number of objects selected

We need to find 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times

¹⁰P₅=10!/(10-5)!

=10!/5!

=10×9×8×7×6×5!/5!

=30240

Hence, 30240 are 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times

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3/20, or 0.15 of the shirts each evening

1 - 1/4 = 3/4

(3/4) / 5 = (3/4) / (5/1) = (3/4) x (1/5) = 3/20 = 0.15

a. The elasticity of demand is 0.0225.

b. Demand is inelastic over this price range.

c. Total revenue would increase due to the more elastic demand resulting in a greater quantity demanded with a price decrease.

Let's first calculate the price elasticity of demand using the midpoint method:

a. Price elasticity of demand formula:

[tex]\[ E_d = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}} \times \frac{\text{Average price}}{\text{Average quantity}} \][/tex]

Percentage change in quantity demanded:

[tex]\[ \text{Percentage change in quantity demanded} = \frac{300 - 100}{\frac{300 + 100}{2}} \times 100\% = \frac{200}{200} \times 100\% = 100\% \][/tex]

Percentage change in price:

[tex]\[ \text{Percentage change in price} = \frac{1.25 - 1.75}{\frac{1.25 + 1.75}{2}} \times 100\% = \frac{-0.5}{1.5} \times 100\% = -33.33\% \][/tex]

Average price and average quantity:

[tex]\[ \text{Average price} = \frac{1.25 + 1.75}{2} = \frac{3}{2} = 1.50 \]\[ \text{Average quantity} = \frac{300 + 100}{2} = \frac{400}{2} = 200 \][/tex]

Now, we can plug these values into the elasticity formula:

[tex]\[ E_d = \frac{100\%}{-33.33\%} \times \frac{1.50}{200} \]\[ E_d = -3 \times 0.0075 \]\[ E_d = -0.0225 \][/tex]

a. The elasticity of demand is 0.0225.

b. Since the elasticity of demand is less than 1, demand is inelastic over this price range.

c. If demand had the same elasticity for a price decline from $1.25 to $0.75 as it does for the decline from $1.75 to $1.25, cutting the price from $1.25 to $0.75 would increase Danny's total revenue because the demand would be more elastic, resulting in a greater increase in quantity demanded compared to the decrease in price.

Complete Question:

Danny “Dimes” Donahue is a neighborhood’s 9-year old entrepreneur. His most recent venture is selling homemade brownies that he bakes himself. At a price of $1.75 each, he sells 100. At a price of $1.25 each, he sells 300.

Instructions: Use the midpoint method and round your answer to 2 decimal places. Do not include a minus sign.

a. What is the elasticity of demand?

b. Is demand elastic or inelastic over this price range?

c. If demand had the same elasticity for a price decline from $ 1.25 to $ 0.75 as it does for the decline from $ 1.75 to $ 1.25, would cutting the price from $ 1.25 to $ 0.75 increase or decrease Danny's total revenue?

The probability that on any given day Jinelle’s bus is on time and Mr. Corney is the driver is (8/15).

Probability is the chance of happening an event or incident.

Given, the probability that Jinelle’s bus is on time is 2/3.

The probability that Mr. Corney is driving the bus is 4/5.

Therefore, the probability that on any given day Jinelle’s bus is on time and Mr. Corney is the driver is:

= (2/3) × (4/5)

= (8/15)

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Subtract the first day of the month from the date of the last Wednesday and divide by 7 to find the remainder. Count backwards from Wednesday to determine the day of the week for the first day of the month, which is Saturday in this case.

The subject of this question pertains to dates and the calendar, which fall under the domain of Mathematics. To answer the question, we need to calculate how many days have passed from the 26th (the last Wednesday) to the 1st day of the same month. A week has seven days so we use the principles of modular arithmetic, a branch of number theory. The 26th day is a Wednesday, and for every seven days we go back, it will still be Wednesday. Thus, the difference from 26 to 1 is 25. Dividing 25 by 7, we get a quotient of 3 and a remainder of 4. This tells us that four days before the last Wednesday, which was the 26th, would be the first day of the month. Going backwards from Wednesday, we count Tuesday (1), Monday (2), Sunday (3), and Saturday (4). Therefore, the first day of that month falls on a Saturday.

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